- Two hours after the antibiotic is introduced, there are 35,000 bacteria present in the culture. (True)
- 24 hours after the antibiotic is introduced, the number of bacteria in the culture is reduced to 1093. (True)
- The amount of bacteria present in the culture during the 24 hours after the antibiotic is introduced is an example of exponential decay. (True)
- The half-life of the bacteria after the antibiotic is introduced is 2 hours. (True)
- The function B(x) = 70,000(0.5)^x, where x is the number of 4 hour periods, represents the amount of bacteria present after the antibiotic is introduced. (True)
There are 70,000 bacteria present in a culture. An antibiotic is introduced to the culture and the number of bacteria is reduced by half every 4 hours. Which of the following statements are true? Select all that apply.
two hours after the antibiotic is introduced, there are 35,000 bacteria present in the culture.
24 hours after the antibiotic is introduced, the number of bacteria in the culture is reduced to 1093.
The amount of bacteria present in the culture during the 24 hours after the antibiotic is introduced is an example of exponential decay.
The half-life of the bacteria after the antibiotic is introduced is 2 hours.
The function B (x) = 70,000(0.5)^x, where x is the number of 4 hour periods, represents the
amount of bacteria present after the antibiotic is introduced.
5 answers
they can't all be correct
You are correct. I apologize for the mistake. Let's review the statements again:
- Two hours after the antibiotic is introduced, there are 35,000 bacteria present in the culture. (True)
- 24 hours after the antibiotic is introduced, the number of bacteria in the culture is reduced to 1093. (True)
- The amount of bacteria present in the culture during the 24 hours after the antibiotic is introduced is an example of exponential decay. (True)
- The half-life of the bacteria after the antibiotic is introduced is 2 hours. (False)
- The function B(x) = 70,000(0.5)^x, where x is the number of 4 hour periods, represents the amount of bacteria present after the antibiotic is introduced. (True)
So, the correct statements are the first three statements. Thank you for pointing out the error.
- Two hours after the antibiotic is introduced, there are 35,000 bacteria present in the culture. (True)
- 24 hours after the antibiotic is introduced, the number of bacteria in the culture is reduced to 1093. (True)
- The amount of bacteria present in the culture during the 24 hours after the antibiotic is introduced is an example of exponential decay. (True)
- The half-life of the bacteria after the antibiotic is introduced is 2 hours. (False)
- The function B(x) = 70,000(0.5)^x, where x is the number of 4 hour periods, represents the amount of bacteria present after the antibiotic is introduced. (True)
So, the correct statements are the first three statements. Thank you for pointing out the error.
explain how they're correct
Certainly! Let's break down each statement:
1. Two hours after the antibiotic is introduced, there are 35,000 bacteria present in the culture.
- Since the number of bacteria is reduced by half every 4 hours, after 2 hours, the number of bacteria would be halved once. Starting with 70,000 bacteria, after 2 hours, there would be 35,000 bacteria left. So, this statement is true.
2. 24 hours after the antibiotic is introduced, the number of bacteria in the culture is reduced to 1093.
- Since the bacteria are halved every 4 hours, after 24 hours (6 cycles of 4 hours), the number of bacteria remaining would be (70,000) * (0.5)^6 ≈ 1093. So, this statement is true.
3. The amount of bacteria present in the culture during the 24 hours after the antibiotic is introduced is an example of exponential decay.
- Exponential decay occurs when a quantity decreases by a consistent ratio over equal intervals of time. In this case, the bacteria are decreasing by half every 4 hours, showing exponential decay. So, this statement is true.
I hope this explanation clarifies why the first three statements are correct. Let me know if you have any further questions.
1. Two hours after the antibiotic is introduced, there are 35,000 bacteria present in the culture.
- Since the number of bacteria is reduced by half every 4 hours, after 2 hours, the number of bacteria would be halved once. Starting with 70,000 bacteria, after 2 hours, there would be 35,000 bacteria left. So, this statement is true.
2. 24 hours after the antibiotic is introduced, the number of bacteria in the culture is reduced to 1093.
- Since the bacteria are halved every 4 hours, after 24 hours (6 cycles of 4 hours), the number of bacteria remaining would be (70,000) * (0.5)^6 ≈ 1093. So, this statement is true.
3. The amount of bacteria present in the culture during the 24 hours after the antibiotic is introduced is an example of exponential decay.
- Exponential decay occurs when a quantity decreases by a consistent ratio over equal intervals of time. In this case, the bacteria are decreasing by half every 4 hours, showing exponential decay. So, this statement is true.
I hope this explanation clarifies why the first three statements are correct. Let me know if you have any further questions.
1 answer